Analyzing N-body problems in physics requires to approximate high-dimensional functionals, which is rooted in the existence of symmetries. Machine learning algorithms are now able to tackle these problems, by also taking advantage of prior knowledge on multiscale physical symmetries. Deep neural network architectures are particularly effective to do so. The following topics will be covered, while highlighting open problems:
1. Curse of dimensionality for supervised and unsupervised learning
2. Nature of prior information to reduce complexity: multiscale separation, symmetries and invariants
3. Wavelets and invariants to translations, rotations and diffeomorphisms
4. Deep scattering networks
5. Regression of quantum molecular energies in quantum chemistry
6. Unsupervised learning and statistical physics
7. Macro and microcanonical maximum entropy models: applications to Ising, turbulence and cosmology
8. Beyond maximum entropy models: generative deep neural networks